本文選題：視覺皮層 + 復(fù)雜網(wǎng)絡(luò)��； 參考：《鄭州大學(xué)》2016年碩士論文

【摘要】：大腦是目前最高效、最復(fù)雜、最穩(wěn)定的系統(tǒng)之一,復(fù)雜網(wǎng)絡(luò)已經(jīng)成為研究大腦神經(jīng)元連接和腦區(qū)連接的新手段�，F(xiàn)有研究已經(jīng)證明大腦網(wǎng)絡(luò)具有小世界特性,其同時(shí)具備較短的平均路徑長度與較高的聚類系數(shù),分別對(duì)應(yīng)大腦信息處理的功能分化與功能整合兩個(gè)基本組織原則。視覺皮層存在于大腦的多個(gè)區(qū)域,是研究大腦的突破口。大腦內(nèi)突觸連接數(shù)量是按照一種先增后減的模式發(fā)展,大腦皮層的突觸剪除機(jī)制可能是大腦網(wǎng)絡(luò)高效穩(wěn)健的關(guān)鍵所在,這也為創(chuàng)建高效率低能耗的網(wǎng)絡(luò)提供新的參考方法。此外,神經(jīng)系統(tǒng)中大多數(shù)的神經(jīng)連接是短的,也存在少量長程連接。導(dǎo)致出現(xiàn)這種結(jié)構(gòu)的內(nèi)在機(jī)制還不清楚,同時(shí)考慮信息傳遞步數(shù)和總體布線代價(jià)的最小化,可能存在距離優(yōu)先連接與大神經(jīng)元優(yōu)先連接的折衷。本文首先利用網(wǎng)絡(luò)的數(shù)學(xué)描述驗(yàn)證視覺皮層網(wǎng)絡(luò)的小世界特性,在此基礎(chǔ)上研究視覺皮層的突觸剪除機(jī)制與突觸連接演化機(jī)制,研究內(nèi)容概括如下:一、在大腦嚴(yán)格的空間限制下基于大腦體素坐標(biāo)建立節(jié)點(diǎn)的位置信息,然后依據(jù)皮層組織結(jié)構(gòu)特性,引入視覺皮層中節(jié)點(diǎn)間的空間距離的計(jì)算方式,建立節(jié)點(diǎn)間的連接概率函數(shù)的數(shù)學(xué)模型。在局部和全局范圍內(nèi)對(duì)視覺皮層網(wǎng)絡(luò)進(jìn)行模擬,驗(yàn)證了視覺皮層網(wǎng)絡(luò)的小世界特性。二、以大腦皮層網(wǎng)絡(luò)的突觸剪除機(jī)制為啟發(fā),設(shè)計(jì)了網(wǎng)絡(luò)減邊演化算法。實(shí)驗(yàn)結(jié)果表明,該算法能夠有效模擬突觸剪除機(jī)制,并且演化后的網(wǎng)絡(luò)會(huì)出現(xiàn)中心節(jié)點(diǎn)、小世界特性和高效率代價(jià)比等性質(zhì)。驗(yàn)證了突觸剪除機(jī)制可能是大腦網(wǎng)絡(luò)高效性的關(guān)鍵所在這一推測(cè)。三、為模擬視覺皮層中總體布線代價(jià)和信息傳遞效率的權(quán)衡機(jī)制,結(jié)合復(fù)雜網(wǎng)絡(luò)動(dòng)態(tài)演化博弈理論,建立了基于距離與大神經(jīng)元優(yōu)先的網(wǎng)絡(luò)演化博弈模型。實(shí)驗(yàn)結(jié)果顯示,演化后的網(wǎng)絡(luò)用長程邊替代了一部分近鄰邊,改變了網(wǎng)絡(luò)的拓?fù)浣Y(jié)構(gòu)和統(tǒng)計(jì)特征。演化博弈穩(wěn)定于合作者占多數(shù)的狀態(tài)時(shí),網(wǎng)絡(luò)出現(xiàn)相對(duì)較少的長程連接,這反應(yīng)了距離優(yōu)先機(jī)制。演化博弈穩(wěn)定于完全背叛狀態(tài)時(shí),網(wǎng)絡(luò)出現(xiàn)較多的長程連接,并會(huì)出現(xiàn)hub節(jié)點(diǎn),這反應(yīng)了大神經(jīng)元優(yōu)先機(jī)制。模型能夠比較真實(shí)的模擬視覺皮層中布線代價(jià)和處理步驟最小化的折中關(guān)系。
[Abstract]:The brain is one of the most efficient, complex and stable systems at present. Complex networks have become a new method to study the connections of brain neurons and brain regions. It has been proved that the brain network has small world characteristics, which has shorter average path length and higher clustering coefficient, corresponding to the two basic organizing principles of functional differentiation and functional integration of brain information processing, respectively. The visual cortex, which exists in multiple regions of the brain, is a breakthrough in the study of the brain. The number of synaptic connections in the brain develops according to a pattern of first increasing and then decreasing. The mechanism of synaptic deletion in the cerebral cortex may be the key to the high efficiency and robustness of the brain network, which also provides a new reference method for the creation of high efficiency and low energy consumption networks. In addition, most neural connections in the nervous system are short and there are a few long-range connections. The internal mechanism leading to this kind of structure is not clear, and considering the minimization of the number of information transfer steps and the total routing cost, there may be a compromise between distance priority connection and large neuron priority connection. In this paper, we first use the mathematical description of the network to verify the small-world characteristics of the visual cortical network, and then study the mechanism of synaptic cutting and synaptic connection evolution of the visual cortex. The research contents are summarized as follows: 1. Under the strict space limit of the brain, the location information of the nodes is established based on the voxel coordinates of the brain, and then the spatial distance between the nodes in the visual cortex is calculated according to the structural characteristics of the cortex. The mathematical model of the connection probability function between nodes is established. The visual cortical network is simulated in the local and global scope to verify the small-world characteristics of the visual cortical network. Secondly, an evolutionary algorithm of network edge reduction is designed based on the synaptic cutting mechanism of cerebral cortex network. The experimental results show that the proposed algorithm can effectively simulate the mechanism of synapse cutting, and the evolved network will have some properties such as central nodes, small-world characteristics and high efficiency / cost ratio. It is proved that synaptic cutting mechanism may be the key to the efficiency of brain network. Thirdly, in order to simulate the tradeoff mechanism of overall routing cost and information transmission efficiency in visual cortex, a network evolutionary game model based on distance and large neuron priority is established based on the dynamic evolution game theory of complex network. The experimental results show that the evolved network uses long range edges to replace some of the nearest neighbor edges and changes the topological structure and statistical characteristics of the network. When the evolutionary game is stable in the state where the collaborators are the majority, there are relatively few long-distance connections in the network, which reflects the distance priority mechanism. When the evolutionary game is stable in the state of complete betrayal, there are more long-distance connections and hub nodes in the network, which reflects the mechanism of large neuron priority. The model can simulate the tradeoff between routing cost and processing steps in visual cortex.
【學(xué)位授予單位】：鄭州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：O157.5;R338

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